Background <p>The two-period randomised crossover design can be advantageous over the parallel-group randomised controlled design with two study arms, yielding greater statistical power and requiring smaller sample sizes. However, a general assumption of the crossover design is that study participants return to their stable baseline state after the experimental treatment has been withdrawn, either immediately or following a wash-out period.</p> Main body <p>In this article, we describe an alternative paradigm for the crossover design, which assumes that participants do not return to their baseline after the experimental treatment has discontinued—in other words, a paradigm under which a persistent carry-over effect is anticipated and even desired after intervention cessation. Such a paradigm is suitable, for example, when investigating behaviour change interventions that aim to establish long-lasting health behaviours through, for example, patient education or counselling. We present sample size calculations and statistical simulations to illustrate that under this alternative paradigm, the randomised crossover design can still maintain greater power than the parallel-group randomised controlled design. Statistical simulations show that, under realistic assumptions of partial or full carry-over, the crossover design can maintain equal or greater power than the parallel-group design, particularly when between-subject heterogeneity is non-negligible.</p> Conclusion <p>Trialists may consider this approach when the nature or intention of the experimental treatment is contrary to the assumption of return to baseline.</p>